Support
Answer and teaching response
1/6 · Six equal half-by-third tiles fill a square metre; this panel uses one.
Plan a panel with fractional side lengths
Produce a coverage record that separates fractional side lengths from square units and checks a material-area claim.
Get student and teacher materialsPrepare the group
Learning goal: Calculate a fractional rectangle's area using equal small tiles, then state what a material-area calculation can and cannot establish.
You will need: Squared paper and pencil. All rectangles are exact flat mathematical models; ignore joints, gaps and cutting loss.
Work through an example
A rectangular display panel is 3/4 metre wide and 2/3 metre high. What area needs covering?
1/2 square metre. Divide a square metre into fourths across and thirds vertically. Each tile is 1/12 square metre; the panel contains six such tiles.
- Name the reference square: it is 1 metre by 1 metre. The panel's width and height are lengths, while the requested coverage is an area.
- Partition the reference into 4 equal columns and 3 equal rows. One small tile has dimensions 1/4 metre by 1/3 metre, so twelve tiles fill one square metre.
- Select 3 columns and 2 rows. The panel contains 3 × 2 = 6 tiles, each with area 1/12 square metre; the total is 6/12, or 1/2 square metre.
- Check with multiplication: 3/4 × 2/3 = 6/12. Both side lengths are below one metre, and the area fits within the reference square. Adding the side lengths would measure a length, not coverage.
Run the 15-minute workshop
- 3 minutes. Ask learners to distinguish the edge length they can trace from the area they can shade.
- 4 minutes. Draw the 4-by-3 reference grid and mark the six tiles used by the panel. Label a tile's area.
- 5 minutes. Choose a support or core item, then compare its product with the dimensions before attempting the challenge.
- 3 minutes. Complete the independent area check and describe why area alone does not prove an uncut sheet fits.
A useful error to discuss
A learner might say: Add 3/4 and 2/3 because both lengths belong to the panel.
Ask what the result must measure. Trace one side for length, then shade the inside for area. Counting small equal tiles explains why two length factors produce square units.
Practise at your level, then check independently
Start with support or core practice, then try the challenge. Complete the independent check without help. Enter a number, fraction or mixed number, such as 3/4 or 1 1/4. The number check does not assess your drawing or explanation.
Core
Answer and teaching response
2/5 · Six of fifteen equal tiles cover the panel: 6/15 = 2/5 square metre.
Challenge
Answer and teaching response
1 1/8 · The longer side includes more than one metre: 3/2 × 3/4 = 9/8 square metres.
Independent check
Answer and teaching response
2/3 · Twenty of thirty equal tiles cover the panel, so the area is 20/30 = 2/3 square metre.
Transfer the idea
A sheet and a panel have equal areas. Does that alone prove the sheet can cover the panel without cutting or gaps?
Discuss a possible response
No. Shape and side lengths also matter. For example, a 1 m by 1/2 m sheet and the worked 3/4 m by 2/3 m panel both have area 1/2 square metre, but the uncut sheet does not contain the panel in either edge-aligned orientation.
Choose the next teaching step
- Uses square units for area and explains the unit tile.
- Distinguishes an area calculation from an actual fitting claim.
Support: Give a unit-square grid already divided into the needed rows and columns; identify one tile before counting the selected region.
Extend: Find a different pair of side lengths with area 1/2 square metre and compare whether the same uncut sheet fits.
Materials for your group
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